From child prodigy to chief scientist

The reviewers' comments for Chapter 101 are out.

"Let's go to the computer room and verify the accuracy again."

Xu Xiao led the still somewhat dazed Pan Hong to the computer room, and quickly started writing the program again, and then began to verify it.

Unsurprisingly, the results of this verification were indeed very satisfactory.

In terms of accuracy, the new lower bound is significantly improved compared to the previous one, with an error of less than 2% compared to the actual numerical results.

In today's world, such high precision is not only the most accurate result in this direction, but it is no exaggeration to call it a milestone improvement.

With such numerical verification results as a basis, the entire result becomes very convincing.

Emerging from the computer room, Pan Hong felt as if Xu Xiao had carried her on her back.

Pan Hong originally only wanted to collaborate with Xu Xiao to solve this problem. Even if there were some differences in their abilities, there shouldn't have been such a significant imbalance.

In the earlier tasks, the two did indeed work together, but when faced with more difficult problems, Xu Xiao clearly demonstrated an even more terrifying mathematical ability.

Without my participation in this project, the research progress might just be slower, but without Xu Xiao, it would probably have been stuck in a state of stagnation for a long time.

"Xu Xiao, this project has reached this stage; it should be nearing completion, right?"

"Yes, the main work is almost done, but we can still make it more complete."

"More complete? You mean we should further summarize and generalize this result?"

"That's right, we can generalize this result to any connected graph and see if we can get a general explicit bound."

Based on his experience reading hundreds of mathematical papers, Xu Xiao felt that this work was still very necessary.

If this step can be completed, the entire project will no longer be limited to the case of a single central vertex, but can cover a large class of graph structures, making the entire theory more complete.

After listening to Xu Xiao's explanation, Pan Hong also felt that this made sense, and the two hit it off immediately and continued their research on the generalization and promotion phase.

Over the next few days, the two focused their main efforts on studying the problem.

Initially, they did encounter some new problems. When using mathematical induction to solve this problem, the inductive step experienced an order explosion, with the bound growing much faster than expected, making it impossible to propagate the inductive hypothesis.

However, they quickly found a solution, using a categorized scaling technique to divide the set of natural numbers according to the Ramsey number system—

They were divided into two categories based on their different growth rates.

The fast-growing set S is scaled using a tighter logarithmic lower bound to control the excessively rapid growth rate.

The slowly growing set T uses a loose linear lower bound scaling, which avoids introducing additional errors.

The scaling results of these two types of sets eventually converge to the same asymptotic order, which perfectly solves the divergence problem of the inductive step.

In this way, they can obtain a general explicit upper bound on the Ramsey number for any connected graph and a complete graph, extending the result from the specific wheel graph to the entire family of connected graphs.

With the project progressing to this point, it's finally time to prepare for its conclusion.

Under Xu Xiao's guidance, the two of them compiled these research findings into a paper.

While writing her thesis, Pan Hong had a vague feeling.

Xu Xiao seemed to be very experienced in writing papers, and she had a very clear understanding of many things that I didn't know.

However, Pan Hong didn't think much of it, only assuming that Xu Xiao must have read a lot of academic papers to be so knowledgeable about these things.

After writing the first draft of the paper, Pan Hong and Xu Xiao talked about submitting the paper.

"Xu Xiao, should we submit this paper ourselves? Which journal would be best to submit it to?"

Xu Xiao is not particularly skilled at choosing journals, nor does she prefer to submit papers herself.

"I think it would be better to submit it under the name of the lab. We're not even students at Yenching University yet, so submitting it directly would likely be a waste of time."

However, if you have a lab and a mentor to vouch for you, the situation will be completely different.

Of course, once Xu Xiao has accumulated enough achievements and gained a certain reputation in the academic community, he can certainly consider submitting papers as the corresponding author.

"So—Xu Xiao, which lab should we send the package through?"

Although several teachers had contacted Pan Hong before, expressing their willingness to take her on as a student, Pan Hong was not in a hurry to choose a mentor immediately.

"If you don't have any questions, let's choose Professor Yuan."

"Professor Yuan Jiyang? Hmm, I think so too."

Yuan Jiyang is indeed one of Pan Hong's ideal mentor choices for the future. When Pan Hong listened to Yuan Jiyang's report at the CMO meeting before, she was quite satisfied with his abilities.

In addition, Yuan Jiyang did not give her a particularly difficult-to-get-along-with feeling; he was quite approachable, which was also a factor that Pan Hong cared about.

After making this arrangement, Xu Xiao informed Yuan Jiyang in advance that she had something she wanted to discuss with him in person.

Once they confirmed that his time was convenient, Xu Xiao and Pan Hong went to Yuan Jiyang's office together.

"Xu Xiao, you're here. Oh—Pan Hong, you came along too?"

Yuan Jiyang recognized Pan Hong; it was impressive that a 15-year-old girl could get a perfect score in CMO.

However, Xu Xiao's deeds are indeed more eye-catching, which is why Pan Hong has not received as much attention.

Before Xu Xiao could even mention her own situation, Yuan Jiyang excitedly told her, "By the way, I have some good news for you. I just received the review comments from *Acta Arithmetica*. Overall, the reviewers are quite satisfied with the paper; it only needs minor revisions and it should be ready for publication."

Upon hearing Yuan Jiyang's words, Xu Xiao couldn't help but show a look of joy, knowing what this news meant.

Normally, SCI journals have a very high rejection rate, often rejecting about half of the manuscripts during the initial review.

When the paper enters the external review stage, these professional reviewers become even more rigorous, and it is quite normal for 80% to 90% of the papers to be rejected.

Even if it requires major revisions before it can be published, it is already an acceptable result for many researchers.

For Xu Xiao's case, where minor revisions are all that's needed before publication, this is generally the most satisfactory type of peer review feedback.